In order to group the curves into clusters, the first 10 PC scores are clustered by a k-means algorithm. In order to evaluate an appropriate number of clusters, Figure 1 shows an elbow plot for \(k \in \{1,...,10\}\):
The elbow plot would indicate an elbow at \(k=2\). However, given the data structure with four scenarios, in the following, \(k=4\) is chosen. The four clusters are rather unbalanced and dominated by two large clusters, namely clusters 3 and 4, as the following table indicates:
| Control | SSP1-RCP2.6 | SSP3-RCP7.0 | SSP5-RCP8.5 | Sum | |
|---|---|---|---|---|---|
| Cluster 1 | 47 | 177 | 204 | 224 | 652 |
| Cluster 2 | 83 | 50 | 55 | 49 | 237 |
| Cluster 3 | 68 | 46 | 58 | 65 | 237 |
| Cluster 4 | 236 | 169 | 145 | 127 | 677 |
| Sum | 434 | 442 | 462 | 465 | 1803 |
In order to get a first impression of the cluster-specific PFT-behavior, Figure 2 shows the PFT-wise mean shares of above ground carbon over the first 100 years of recovery. Note that here, the clusters are derived using the whole time span of 126 years of recovery and all scenarios are combined.
Figure 3 shows the spatial distribution of the clusters: